Structural, electronic and mechanical properties of all-sp2 carbon allotropes with density lower than graphene

In this work we propose a few novel energetically and dynamically stable all- carbon-based architectures with low density obtained by augmenting planar three-coordinated uniform tessellations. Using geometrical packing arguments, we show that such arrangements satisfy the locally–jammed packing condition and represent some of the least dense structures of all- bonded carbon allotropes that could ever be synthesised. We fully characterize from first principles these new architectures, by assessing i) the electronic properties, such as the band structure and the density of states; ii) the dynamical characteristics, such as the phonon dispersion; and iii) the mechanical properties, such as the elastic constants and the stress–strain relationships. We compare our findings with already synthesised carbon-based materials, in particular graphene, and we find that in the lowest–density structures the mechanical rigidity is considerably depleted, while other specific mechanical characteristics, such as toughness and strength, are comparable to the relevant specific values of graphene. Furthermore, a flat band at the Fermi level emerges in the electronic band structure of the augmented geometries, which is a feature similarly appearing in Kagome lattices.